Problem: Umaima is 5 times as old as Emily. Four years ago, Umaima was 7 times as old as Emily. How old is Emily now?
Solution: We can use the given information to write down two equations that describe the ages of Umaima and Emily. Let Umaima's current age be $u$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $u = 5e$ Four years ago, Umaima was $u - 4$ years old, and Emily was $e - 4$ years old. The information in the second sentence can be expressed in the following equation: $u - 4 = 7(e - 4)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to use our first equation for $u$ and substitute it into our second equation. Our first equation is: $u = 5e$ . Substituting this into our second equation, we get: $5e$ $-$ $4 = 7(e - 4)$ which combines the information about $e$ from both of our original equations. Simplifying the right side of this equation, we get: $5 e - 4 = 7 e - 28$ Solving for $e$ , we get: $2 e = 24.$ $e = 12$.